Numerical Methods for the Life Scientist

Beschreibung

Beschreibung

Enzyme kinetics, binding kinetics and pharmacological dose-response curves are currently analyzed by a few standard methods. Some of these, like Michaelis-Menten enzyme kinetics, use plausible approximations, others, like Hill equations for dose-response curves, are outdated. Calculating realistic reaction schemes requires numerical mathematical routines which usually are not covered in the curricula of life science. This textbook will give a step-by-step introduction to numerical solutions of non-linear and differential equations. It will be accompanied with a set of programs to calculate any reaction scheme on any personal computer. Typical examples from analytical biochemistry and pharmacology can be used as versatile templates. When a reaction scheme is applied for data fitting, the resulting parameters may not be unique. Correlation of parameters will be discussed and simplification strategies will be offered.

Inhaltsverzeichnis

IntroductionClassical enzyme kineticsClassical dose-response curves and the Hill coefficientClassical association and dissociation kinetics and exponential fitsNumerical methodsPreparing the computerInstallation of Octave for different platformsInstallation of LinuxRunning the provided programsData input and outputBinding equilibriaAnalytical and numerical solution for equilibrium binding to one siteEquilibrium binding to two or more sites.Equilibrium binding to two or more conformational statesEquilibrium binding for oxygen to hemoglobin (MWC model)Equilibrium binding of more than one ligand (e.g. agonist and inhibitor)Enzyme kinetics as coupled equilibriaEnzyme kinetics with competitive or noncompetitive inhibitorsDose-response curves for receptor agonists and enzyme inhibitorsBinding kineticsLigand binding kinetics of first and second orderNumerical solutions of differential equationsCalculation of true enzyme kineticsDissociation by dilution and dissociation by competition ("chase")States and sitesLeast squares fit to experimental dataThe function lsqcurvefitComparing correct binding curves with Hill equationsComparing real binding kinetics with current multi-exponential fitsFitting experimental dataCauses for errorsMulti-parameter fitsCorrelation of parametersSelecting a model and minimizing the number of parametersDegrees of freedomGlobal FitsSignificance of parameters in multi-parameter fitsComparing the two different approachesModel independent versus model calculationsGlobal fit versus single fitsMake ends meet: Try to analyze reported data with new methodsDesigning experiments for complete analysisAppendixDescription of program filesSample dataComparing MATLAB and Octave code